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Bayesian inference with INLA

The integrated nested Laplace approximation (INLA) is a recent computational method that can fit Bayesian models in a fraction of the time required by typical Markov chain Monte Carlo (MCMC) methods. INLA focuses on marginal inference on the model parameters of latent Gaussian Markov random fields models and exploits conditional independence properties in the model for computational speed. Les mer
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Leveringstid: Sendes innen 21 dager
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Om boka

The integrated nested Laplace approximation (INLA) is a recent computational method that can fit Bayesian models in a fraction of the time required by typical Markov chain Monte Carlo (MCMC) methods. INLA focuses on marginal inference on the model parameters of latent Gaussian Markov random fields models and exploits conditional independence properties in the model for computational speed.





Bayesian Inference with INLA provides a description of INLA and its associated R package for model fitting. This book describes the underlying methodology as well as how to fit a wide range of models with R. Topics covered include generalized linear mixed-effects models, multilevel models, spatial and spatio-temporal models, smoothing methods, survival analysis, imputation of missing values, and mixture models. Advanced features of the INLA package and how to extend the number of priors and latent models available in the package are discussed. All examples in the book are fully reproducible and datasets and R code are available from the book website.





This book will be helpful to researchers from different areas with some background in Bayesian inference that want to apply the INLA method in their work. The examples cover topics on biostatistics, econometrics, education, environmental science, epidemiology, public health, and the social sciences.

Fakta

Innholdsfortegnelse

Introduction to Bayesian Inference
Introduction


Bayesian inference


Conjugate priors


Computational methods


Markov chain Monte Carlo


The integrated nested Laplace approximation


An introductory example: U's in Game of Thrones books


Final remarks









The Integrated Nested Laplace Approximation



Introduction


The Integrated Nested Laplace Approximation


The R-INLA package


Model assessment and model choice


Control options


Working with posterior marginals


Sampling from the posterior









Mixed-effects Models



Introduction


Fixed-effects models


Types of mixed-effects models


Information on the latent effects


Additional arguments


Final remarks









Multilevel Models



Introduction


Multilevel models with random effects


Multilevel models with nested effects


Multilevel models with complex structure


Multilevel models for longitudinal data


Multilevel models for binary data


Multilevel models for count data









Priors in R-INLA



Introduction


Selection of priors


Implementing new priors


Penalized Complexity priors


Sensitivity analysis with R-INLA


Scaling effects and priors


Final remarks









Advanced Features



Introduction


Predictor Matrix


Linear combinations


Several likelihoods


Shared terms


Linear constraints


Final remarks






Spatial Models



Introduction


Areal data


Geostatistics


Point patterns









Temporal Models



Introduction


Autoregressive models


Non-Gaussian data


Forecasting


Space-state models


Spatio-temporal models


Final remarks









Smoothing



Introduction


Splines


Smooth terms with INLA


Smoothing with SPDE


Non-Gaussian models


Final remarks









Survival Models



Introduction


Non-parametric estimation of the survival curve


Parametric modeling of the survival function


Semi-parametric estimation: Cox proportional hazards


Accelerated failure time models


Frailty models


Joint modeling









Implementing New Latent Models



Introduction


Spatial latent effects


R implementation with rgeneric


Bayesian model averaging


INLA within MCMC


Comparison of results


Final remarks









Missing Values and Imputation



Introduction


Missingness mechanism


Missing values in the response


Imputation of missing covariates


Multiple imputation of missing values


Final remarks










13. Mixture models









Introduction


Bayesian analysis of mixture models


Fitting mixture models with INLA


Om forfatteren